Operational Quantum Reference Frame Transformations
- URL: http://arxiv.org/abs/2303.14002v2
- Date: Tue, 19 Dec 2023 10:07:07 GMT
- Title: Operational Quantum Reference Frame Transformations
- Authors: Titouan Carette, Jan G{\l}owacki and Leon Loveridge
- Abstract summary: We provide a general, operationally motivated framework for quantum reference frames and their transformations.
The work is built around the notion of operational equivalence.
We give an explicit realisation in the setting that the initial frame admits a highly localized state with respect to the frame observable.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum reference frames are needed in quantum theory for much the same
reasons as reference frames are in classical relativity theories: to manifest
invariance in line with fundamental relativity principles. Though around since
the 1960s, and used in a wide range of applications, only recently has the
means for transforming descriptions between different frames been tackled in
detail. Such transformations are needed for an internally consistent theory of
quantum reference frames. In this work, we provide a general, operationally
motivated framework for quantum reference frames and their transformations,
holding for locally compact groups. The work is built around the notion of
operational equivalence, in which theoretical objects that cannot be physically
distinguished are identified. For example, we describe the collection of
observables relative to a given frame as a subspace of the algebra of
invariants on the composite of system and frame, and from here the set of
relative states can be constructed as a convex subset of the predual. Besides
being invariant, the relative observables are also framed, meaning that they
can be realized with the chosen frame observable. The frame transformations are
then maps between equivalence classes of relative states that can be
distinguished by both initial and final frames. We give an explicit realisation
in the setting that the initial frame admits a highly localized state with
respect to the frame observable. The transformations are invertible exactly
when the final frame also has such a localizability property. The procedure we
present is in operational agreement with other recent inequivalent
constructions on the domain of common applicability, but extends them in a
number of ways which we describe.
Related papers
- A Canonization Perspective on Invariant and Equivariant Learning [54.44572887716977]
Canonization provides a principled understanding of the design of frames.
We show that there exists an inherent connection between frames and canonical forms.
We design novel frames for eigenvectors that are strictly superior to existing methods.
arXiv Detail & Related papers (2024-05-28T17:22:15Z) - Quantum Reference Frames from Top-Down Crossed Products [0.0]
Crossed product is a way to realize quantum reference frames from the bottom-up.
We show that one cannot obtain in quantumequivalent reference frames using this approach.
We term this algebra the G-framed algebra, and show how potentially inequivalent frames are realized within this object.
arXiv Detail & Related papers (2024-05-22T18:00:01Z) - Operational Quantum Frames: An operational approach to quantum reference
frames [0.0]
We introduce an operational notion of a quantum reference frame -- which is defined as a quantum system equipped with a covariant positive operator-valued measure (POVM)
We show that when the frame is localizable, meaning that it allows for states that give rise to a highly localized probability distribution of the frame's observable, by restricting the relative description upon such localized frame preparation we recover the usual, non-relational formalism of quantum mechanics.
arXiv Detail & Related papers (2023-04-14T09:30:35Z) - Non-standard entanglement structure of local unitary self-dual models as
a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry.
We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
arXiv Detail & Related papers (2021-11-29T23:37:58Z) - Relative subsystems and quantum reference frame transformations [0.0]
We derive quantum reference frame transformations from first principles, using only standard quantum theory.
We find more general transformations than those studied so far, which are valid only in a restricted subspace.
Our framework contains additional degrees of freedom in the form of an "extra particle," which carries information about the quantum features of reference frame states.
arXiv Detail & Related papers (2021-10-25T18:23:28Z) - Quantum reference frames: derivation of perspective-dependent
descriptions via a perspective-neutral structure [0.0]
We develop a symmetry-inspired approach to describe physics from the perspective of quantum reference frames.
We show that the operationally meaningful perspective dependent descriptions are given by Darboux coordinates on the constraint surface.
We conclude by constructing a quantum perspective neutral structure, via which we can derive and change perspective dependent descriptions.
arXiv Detail & Related papers (2021-09-04T18:09:07Z) - Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
Two particles are identical if all their intrinsic properties, such as spin and charge, are the same.
Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles.
We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
arXiv Detail & Related papers (2021-05-10T13:11:59Z) - Quantum Relativity of Subsystems [58.720142291102135]
We show that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement.
Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra.
Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent.
arXiv Detail & Related papers (2021-03-01T19:00:01Z) - Equivalence of approaches to relational quantum dynamics in relativistic
settings [68.8204255655161]
We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector.
We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
arXiv Detail & Related papers (2020-07-01T16:12:24Z) - There is only one time [110.83289076967895]
We draw a picture of physical systems that allows us to recognize what is this thing called "time"
We derive the Schr"odinger equation in the first case, and the Hamilton equations of motion in the second one.
arXiv Detail & Related papers (2020-06-22T09:54:46Z) - Quantum reference frames for general symmetry groups [0.0]
We introduce a relational formalism which identifies coordinate systems with elements of a symmetry group $G$.
This generalises the known operator for translations and boosts to arbitrary finite groups, including non-Abelian groups.
We prove a theorem stating that the change of quantum reference frame consistent with these principles is unitary if and only if the reference systems carry the left and right regular representations of $G$.
arXiv Detail & Related papers (2020-04-29T16:16:53Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.